In “We’re going to throw a surprise party for her”, is "for her" an adjectival phrase or an adverbial phrase?

1. "For her, we're going to throw a surprise party".
2. "For Anne, I'll get some flowers".

If rephrased this way, then both can be adverbial as they modify the whole sentence. They can be adverbial in nature, too, if you replaced them with an adverb like "tomorrow".

1. We're going to throw a surprise party [tomorrow].
2. I'll get some flowers [tomorrow].

I think it ultimately doesn't make a difference. HOW it functions and what part of speech it is are two different things. They are prepositional, no matter what, even if their function is adverbial. That's how I see it.

Both are ambiguous:

• In your first sentence, "for her" can modify either "surprise party" (cf. "This surprise party is for Alice") or "throw a surprise party" (cf. "It was a great surprise party; we threw it for Bob").
• In your second sentence, "for Anne" can modify either "flowers" (cf. "These flowers are for Anne") or "get some flowers" (cf. "These are chrysanthemums; I got them for Anne").

But in both cases, the ambiguity is mostly theoretical; we could contrive a situation where the party's honoree is not the person for whose benefit we're actually throwing it, or where the recipient of the flowers is not the person for whose benefit we're getting them ("These roses are for my boss's wife. He sent me to get them for him from the florist and deliver them to her"), but in most cases the real-world meaning of the sentence is the same under either parse, such that the ambiguity is unlikely to be noticed.